Question

give the product using the appropriate number of significant digits.

\\((217\text{ m})(38\text{ m})(104\text{ m})\\)

Explanation:

Count significant digits of each factor

Identify the significant figures for each given value:

• \(217\text{ m}\) has 3 significant digits.
• \(38\text{ m}\) has 2 significant digits.
• \(104\text{ m}\) has 3 significant digits.

Determine the limiting number of significant digits

For multiplication, the result must have the same number of significant digits as the factor with the fewest significant digits:

• The fewest significant digits is 2 (from \(38\text{ m}\)).

Calculate the raw product

Multiply the numerical values together:

$$ 217 \times 38 \times 104 = 857,464 $$

The units are:

$$ \text{m} \times \text{m} \times \text{m} = \text{m}^3 $$

Round to the correct number of significant digits

Round \(857,464\) to 2 significant digits:

• The first two significant digits are 8 and 5.
• The third digit is 7, which is 5 or greater, so round up the second digit from 5 to 6.
• This gives \(860,000\text{ m}^3\).

Answer:

Give the product using the appropriate number of significant digits.

\((217\text{ m})(38\text{ m})(104\text{ m}) =\) <blank>\(860,000\)</blank> \(\text{m}^3\)